Some properties of multivariate extreme value distributions and multivariate tail equivalence
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Denote byH ak-dimensional extreme value distribution with marginal distributionHi(x)=Λ(x)=exp(−e−x),x∈R1. Then it is proved thatH(x)=Λ(x1)...Λ(xk) for anyx=(x1, ...,xk) ∈Rk, if and only if the equation holds forx=(0,...,0). Next some multivariate extensions of the results by Resnick (1971,J. Appl. Probab.,8, 136–156) on tail equivalence and asymptotic distributions of extremes are established.
Key words and phrasesMultivariate extreme value distribution multivariate tail equivalence
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- de Haan, L. (1970).On Regular Variation and Its Application to the Weak Convergence of Sample Extremes, Mathematical Centre Tracts, Vol. 32, Amsterdam.Google Scholar